The OED seems to express that it was not so much who barbarians were, but who they were not. They were not Greek.There is probably a tie-in that the northern coast of Africa was known as the Barbary States.

There is a step missing in this etymology, I think. In Latin "barbarian" only means "non-Roman" and was not originally pejorative.

The Greek/Latin word "barba" means "beard" (cf. English "barber"), and since Greek and Roman soldiers were required to be clean-shaven (until the Emperor Hadrian grew a beard), it seems likely this is the direct origin of the word "barbarian". Perhaps "barba" then came from the "bar bar" sound made by those that didn't speak Greek.

My classics teacher supported the theory that the Greeks named other non-Greek tribes as barbarians because of the bar-bar sound of their speech. In Alexandrine times the saying of "all non-Greeks are barbarians" was used by all those who had classical education often as a put-down to the uneducated hoi polloi. However I do not think that the origin of barbarian had much to do with the beards of the non-Greek tribes as the Greeks themselves did grow beards, as one can see on the depictions of battles and heroes on the plethora of ancient Greek pottery and statues.

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